Smirke came from a family of artists. His father, also Robert (1752-1845), was a historical painter and book illustrator. His younger brother Sydney (1798-1877) was an architect.
Although Smirke worked on private buildings in the Gothic Revival and Medieval styles, he is best known as an architect of public Neo-Classical/Greek Revival buildings. His first commission was Lowther Castle built in 1806 when he was an inexperienced young man of 25. The British Museum (1823 -1847) and Canada House (1824), both in London are two of his best known public buildings.
Smirke was knighted in 1832, and received the RIBA (Royal Institute of British Architects) Gold Medal for Architecture in 1853. He died in Cheltenham on April 18th 1867.